The build-up of the crisis in the Strait of Hormuz took another big step this weekend, when the aircraft carrier USS Abraham Lincoln entered the Persian Gulf together with British and French naval escorts — defying Iran’s warnings not to send another carrier there.

The Lincoln is there in case Iran tries to make good on its threat to close that vital international waterway in response to harsh new US and European Union sanctions against the radical Islamicist regime. What happens next in this high-stakes game depends on three people.

One of them is President Mahmoud Ahmadinejad of Iran. The second is Premier Wen Jiabao of China, who’ll have to decide whether his country is ready to join those sanctions — and by doing so, put the last nail in Tehran’s economic coffin.

The third is President Obama. How he responds to what happens in the Gulf could decide the future shape of the Middle East — not to mention his own re- election.

A dozen supertankers a day and one-third of the world’s seaborne oil pass through the strait. For Ahmadinejad, trying to close it (with mines, anti-ship cruise missiles, midget subs and swarms of suicide attack boats) is a war Iran is bound to lose, given America’s overwhelming military power in the region. Nor will his threats stop the EU from going ahead with sanctions.

No, his most likely intended audience is far to the east in Asia, where economies thrive or wither depending on the flow of oil coming out of the Gulf.

The most important of those is China, which imports 35 percent of its oil needs through the Gulf, including 12 percent from Iran. In exchange, Beijing has given Tehran advanced missile technology, turned a blind eye to Iran’s acquisition of key nuclear-weapons technology from Chinese sources and blocked any tough UN anti-Iran sanctions.

But now Beijing is under pressure from the United States and Europe to end its oil imports from Iran and join the campaign to halt Tehran’s relentless hunt for a nuclear bomb. In December alone, it cut that import total by nearly half.

But Wen and his colleagues worry about what happens if they go on an Iran-free oil diet. Before he commits to the full court press of sanctions, Wen has been meeting with Arab leaders around the Gulf to make sure oil from the Saudis and the Arab Emirates will make up for any shortfall.

Meanwhile, his other eye is on the Strait of Hormuz, as is Japan’s. Any major disruption there will make them think twice about supporting any sanctions, even if it means Iran gets its bomb.

Here’s the dangerous part — and where President Obama comes in.

Even if Iran loses a military confrontation with the United States in the Hormuz Strait, it wins. Tehran can hope that disrupting tanker traffic, even for just a few weeks, and driving up oil prices in the meantime, will convince China and the rest of Asia that sanctions are as deadly a threat to their economy as to Iran’s.

The only way to prevent that is for President Obama to make it clear that, by closing the strait, Ahmadinejad will doom the Islamic Republic. Only if China and the rest of the world believes such a closure could never happen again, will Iran’s threat to international stability finally come an end.

But will Obama do it? There are no easy military solutions for regime change in Iran. Certainly Ahmadinejad is betting that our commander-in-chief won’t use a confrontation in the strait as a pretext for taking out Iran’s nuclear sites, let alone regime change.

Indeed, Obama would know that forcibly reopening the strait would be enough to make him look like the reincarnation of Dwight Eisenhower in time for the 2012 election. But that “victory” might also be enough to panic both Asia and possibly Europe, and wreck any effective sanctions.

Then the world and the Middle East becomes a very dangerous place. A nuclear-arms race in that volatile region becomes inevitable, and Iran — home of state-sponsored terrorism and the yearning for a second Holocaust — looks more impregnable than ever.

The fate of the strait hangs by a thin thread of oil. It’s up to our president and the Navy to make sure that oil flows — and that any regime threatening to cut it never does.

Arthur Herman was a Pulitzer Prize finalist in 2009. His new book, “Freedom’s Forge,” is due in May.